By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established...By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.展开更多
Some sufficient and necessary conditions are given for the equivalence between two crossed product actions of Hopf algebra H on the same linear category, and the Maschke theorem is generalized. Based on the result of ...Some sufficient and necessary conditions are given for the equivalence between two crossed product actions of Hopf algebra H on the same linear category, and the Maschke theorem is generalized. Based on the result of the crossed product in the classic Hopf algebra theory, first, let A be a k-linear category and H be a Hopf algebra, and the two crossed products A#_σH and A#'_σH are isomorphic under some conditions. Then, let A#_σH be a crossed product category for a finite dimensional and semisimple Hopf algebra H. If V is a left A#σH-module and WC V is a submodule such that W has a complement as a left A-module, then W has a complement as a A#_σH-module.展开更多
By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established...By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.展开更多
In a previous study [1] the authors had developed a methodology for predicting global oil production. Briefly, the model accounted for disruptions in production by utilising a series of Hubbert curves in combination w...In a previous study [1] the authors had developed a methodology for predicting global oil production. Briefly, the model accounted for disruptions in production by utilising a series of Hubbert curves in combination with a polynomial smoothing function. Whilst the model was able to produce predictions for future oil production, the methodology was complex in its implementation and not easily applied to future disruptions. In this study a Generalized Bass model approach is incorporated with the Hubbert linearization technique that overcomes these limitations and is consistent with our previous predictions.展开更多
In this paper we generalize the notions of crossed products and L-R smash products in the context of multiplier Hopf algebras. We use comodule algebras to define generalized diagonal crossed products, L-R smash produc...In this paper we generalize the notions of crossed products and L-R smash products in the context of multiplier Hopf algebras. We use comodule algebras to define generalized diagonal crossed products, L-R smash products, two-sided smash products and two-sided crossed products and prove that they are all associative algebras. Then we show the isomorphic relations of them.展开更多
We develop the Radford's biproduct theorem which plays an important role in giving a negative answer to a conjecture of I Kaplansky. Let B, H be two Hopf algebras with H acting weakly on B and α, β : B → H H be...We develop the Radford's biproduct theorem which plays an important role in giving a negative answer to a conjecture of I Kaplansky. Let B, H be two Hopf algebras with H acting weakly on B and α, β : B → H H be two linear maps verifying suitable conditions. We consider in this paper a twisted Hopf crossed coproduct B ×βα H and derive a necessary and sufficient condition for B # ×βα H with a Hopf smash product structure to be a bialgebra which generalizes in [14, Theorem 1.1] and the well-known Radford biproduct theorem [10, Theorem 1] .展开更多
This paper presents generalized CAPP (G-CAPP) method which deals with macro process planning for multiobjective in the planning stage of production line of accuracy welding (PLAW) based on the features of accuracy...This paper presents generalized CAPP (G-CAPP) method which deals with macro process planning for multiobjective in the planning stage of production line of accuracy welding (PLAW) based on the features of accuracy welding production ( AWP ). G-CAPP offers foundations for prototype design and general equipment sorting, production capacity predication and production analysis by means of simulation and optimization. A synthetic hierarchy evaluation (SHE) model for G-CAPP established according to the planning objective is utilized to estimate the alternate processing plans by using membership function and analytic hierarchy process (AHP) of operational theory. The assembly welding line of hydraulic torque converter (HTC) is as an example of typical A WP to explicate G-CAPP and synthetic evaluating strategy of PLAW. The feasible and rational process configuration strategies of HTC assembly welding line are pointed oat under different planning objective.展开更多
Based on the theory of products of generalized topologies,we introduce the product mappings and the diagonal mappings in generalized topological spaces in this paper.We investigate some basic properties(especially,the...Based on the theory of products of generalized topologies,we introduce the product mappings and the diagonal mappings in generalized topological spaces in this paper.We investigate some basic properties(especially,the continuity,openness and closedness)of the product mappings and the diagonal mappings in generalized topological spaces.Some applications are given to answer two questions raised in[3].展开更多
A minimal generalized time-bandwidth product-based coarse-to-fine strategy is proposed with one novel ideas highlighted: adopting a coarse-to-fine strategy to speed up the searching process. The simulation results on ...A minimal generalized time-bandwidth product-based coarse-to-fine strategy is proposed with one novel ideas highlighted: adopting a coarse-to-fine strategy to speed up the searching process. The simulation results on synthetic and real signals show the validity of the proposed method.展开更多
We shall give natural generalized solutions of Hadamard and tensor products equations for matrices by the concept of the Tikhonov regularization combined with the theory of reproducing kernels.
Monitoring of rangeland forage production at specified spatial and temporal scales is necessary for grazing management and also for implementation of rehabilitation projects in rangelands. This study focused on the ca...Monitoring of rangeland forage production at specified spatial and temporal scales is necessary for grazing management and also for implementation of rehabilitation projects in rangelands. This study focused on the capability of a generalized regression neural network(GRNN) model combined with GIS techniques to explore the impact of climate change on rangeland forage production. Specifically, a dataset of 115 monitored records of forage production were collected from 16 rangeland sites during the period 1998–2007 in Isfahan Province, Central Iran. Neural network models were designed using the monitored forage production values and available environmental data(including climate and topography data), and the performance of each network model was assessed using the mean estimation error(MEE), model efficiency factor(MEF), and correlation coefficient(r). The best neural network model was then selected and further applied to predict the forage production of rangelands in the future(in 2030 and 2080) under A1 B climate change scenario using Hadley Centre coupled model. The present and future forage production maps were also produced. Rangeland forage production exhibited strong correlations with environmental factors, such as slope, elevation, aspect and annual temperature. The present forage production in the study area varied from 25.6 to 574.1 kg/hm^2. Under climate change scenario, the annual temperature was predicted to increase and the annual precipitation was predicted to decrease. The prediction maps of forage production in the future indicated that the area with low level of forage production(0–100 kg/hm^2) will increase while the areas with moderate, moderately high and high levels of forage production(≥100 kg/hm^2) will decrease both in 2030 and in 2080, which may be attributable to the increasing annual temperature and decreasing annual precipitation. It was predicted that forage production of rangelands will decrease in the next couple of decades, especially in the western and southern parts of Isfahan Province. These changes are more pronounced in elevations between 2200 and 2900 m. Therefore, rangeland managers have to cope with these changes by holistic management approaches through mitigation and human adaptations.展开更多
The definition of generalized product of fractal is first put forward for the research on the relations between original fractal and its product of fractal when the transformations of iteration function system (IFS)...The definition of generalized product of fractal is first put forward for the research on the relations between original fractal and its product of fractal when the transformations of iteration function system (IFS) are incomplete. Then the representations of generalized product of IFS are discussed based on the theory of the product of fractal. Furthermore, the dimensional relations between the product of fractal and its semi-product are obtained. The dimensional relations of self-similar set are discussed. Finally, the examples for rendering fractal graphs are given. These results posses potentials in image compression and pattern recognition.展开更多
Fermat’s last theorem, had the statement that there are no natural numbers A, B, and C such that A<sup>n</sup> + B<sup>n</sup> = C<sup>n</sup>, in which n is a natural number great...Fermat’s last theorem, had the statement that there are no natural numbers A, B, and C such that A<sup>n</sup> + B<sup>n</sup> = C<sup>n</sup>, in which n is a natural number greater than 2. We have shown that any product of two odd numbers can generate Fermat or Pythagoras triple (A, B, C) following n = 2 and also it is applicable A<sup>2</sup> + B<sup>2</sup> + C<sup>2</sup> + D<sup>2</sup> + so on =A<sub>n</sub><sup>2 </sup>where all are natural numbers.展开更多
In order to study algebraic structures of parallelizable sphere s7, the notions of quasimodules and biquasimodnle algebras over Hopf quasigroups, which are not required to be associative, are introduced. The lack of a...In order to study algebraic structures of parallelizable sphere s7, the notions of quasimodules and biquasimodnle algebras over Hopf quasigroups, which are not required to be associative, are introduced. The lack of associativity of quasimodules is compensated for by conditions involving the antipode. The twisted smash product for Hopf quasigroups is constructed using biquasimodule algebras, which is a generalization of the twisted smash for Hopf algebras. The twisted smash product and tensor coproduct is turned into a Hopf quasigroup if and only if the following conditions (h1→a) h2 = (h2→a) h1, (a←S(h1)) h2 = (a←S(h2)) h1, hold. The obtained results generalize and improve the corresponding results of the twisted smash product for Hopf algebras.展开更多
The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left...The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left weak H-module coalgebra.First,a weak generalized smash coproduct C×lH D over quantum groupoids is defined and the module and comodule structures on it are constructed.The weak generalized right smash coproduct C×rL D is similar.Then some isomorph-isms between them are obtained.Secondly,by introducing some concepts of a weak convolution invertible element,a weak co-inner coaction and a strongly relative co-inner coaction,a sufficient condition for C×rH D to be isomorphic to Cv D is obtained,where v∈WC(C,H)and the coaction of H on D is right strongly relative co-inner.Finally,the duality theorem for a generalized smash coproduct over quantum groupoids,(C×lH H)×lH H≌Cv(H×lH H),is obtained.展开更多
Let k be a commutative ring, C a projective k-coalgebra. The smash productsof entwining structure (A, C)_ψ are discussed. When the map ψ is a bijective, and C is a finitelygenerated k-module, a version of the Ulbric...Let k be a commutative ring, C a projective k-coalgebra. The smash productsof entwining structure (A, C)_ψ are discussed. When the map ψ is a bijective, and C is a finitelygenerated k-module, a version of the Ulbrich theorem for coalgebras C is given.展开更多
This paper gives a sufficient and necessary condition for twisted products to be weak Hopf algebras, moreover, gives a description for smash products to be weak Hopf algebras. It respectively generalizes R.K.Molnar...This paper gives a sufficient and necessary condition for twisted products to be weak Hopf algebras, moreover, gives a description for smash products to be weak Hopf algebras. It respectively generalizes R.K.Molnar's major result and I.Boca's result.展开更多
文摘By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
基金The National Natural Science Foundation of China(No.11371088)the Natural Science Foundation of Jiangsu Province(No.BK2012736)+1 种基金the Fundamental Research Funds for the Central Universitiesthe Research Innovation Program for College Graduates of Jiangsu Province(No.KYLX15_0109)
文摘Some sufficient and necessary conditions are given for the equivalence between two crossed product actions of Hopf algebra H on the same linear category, and the Maschke theorem is generalized. Based on the result of the crossed product in the classic Hopf algebra theory, first, let A be a k-linear category and H be a Hopf algebra, and the two crossed products A#_σH and A#'_σH are isomorphic under some conditions. Then, let A#_σH be a crossed product category for a finite dimensional and semisimple Hopf algebra H. If V is a left A#σH-module and WC V is a submodule such that W has a complement as a left A-module, then W has a complement as a A#_σH-module.
文摘By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
文摘In a previous study [1] the authors had developed a methodology for predicting global oil production. Briefly, the model accounted for disruptions in production by utilising a series of Hubbert curves in combination with a polynomial smoothing function. Whilst the model was able to produce predictions for future oil production, the methodology was complex in its implementation and not easily applied to future disruptions. In this study a Generalized Bass model approach is incorporated with the Hubbert linearization technique that overcomes these limitations and is consistent with our previous predictions.
基金Foundation item: Supported by the Scientific Research Foundation for Doctoral Scientists of Henan University of Science and Technology(09001303) Supported by the National Natural Science Foundation of China(11101128)
文摘In this paper we generalize the notions of crossed products and L-R smash products in the context of multiplier Hopf algebras. We use comodule algebras to define generalized diagonal crossed products, L-R smash products, two-sided smash products and two-sided crossed products and prove that they are all associative algebras. Then we show the isomorphic relations of them.
基金Supported by the NNSF of China(10871042)Supported by the Foster Foundation of Henan Normal University(2010PL01)Supported by the Research Fund of PhD(1005)
文摘We develop the Radford's biproduct theorem which plays an important role in giving a negative answer to a conjecture of I Kaplansky. Let B, H be two Hopf algebras with H acting weakly on B and α, β : B → H H be two linear maps verifying suitable conditions. We consider in this paper a twisted Hopf crossed coproduct B ×βα H and derive a necessary and sufficient condition for B # ×βα H with a Hopf smash product structure to be a bialgebra which generalizes in [14, Theorem 1.1] and the well-known Radford biproduct theorem [10, Theorem 1] .
文摘This paper presents generalized CAPP (G-CAPP) method which deals with macro process planning for multiobjective in the planning stage of production line of accuracy welding (PLAW) based on the features of accuracy welding production ( AWP ). G-CAPP offers foundations for prototype design and general equipment sorting, production capacity predication and production analysis by means of simulation and optimization. A synthetic hierarchy evaluation (SHE) model for G-CAPP established according to the planning objective is utilized to estimate the alternate processing plans by using membership function and analytic hierarchy process (AHP) of operational theory. The assembly welding line of hydraulic torque converter (HTC) is as an example of typical A WP to explicate G-CAPP and synthetic evaluating strategy of PLAW. The feasible and rational process configuration strategies of HTC assembly welding line are pointed oat under different planning objective.
基金Supported by the National Natural Science Foundation of China(11501404)Jiangsu Planned Talent Projects(2016-JY-078)+1 种基金Jiangsu Jiaogai Projects Fundations(2017JSJG490)Jiangsu Qing Lan Project(PY2016006)。
文摘Based on the theory of products of generalized topologies,we introduce the product mappings and the diagonal mappings in generalized topological spaces in this paper.We investigate some basic properties(especially,the continuity,openness and closedness)of the product mappings and the diagonal mappings in generalized topological spaces.Some applications are given to answer two questions raised in[3].
文摘A minimal generalized time-bandwidth product-based coarse-to-fine strategy is proposed with one novel ideas highlighted: adopting a coarse-to-fine strategy to speed up the searching process. The simulation results on synthetic and real signals show the validity of the proposed method.
文摘We shall give natural generalized solutions of Hadamard and tensor products equations for matrices by the concept of the Tikhonov regularization combined with the theory of reproducing kernels.
文摘Monitoring of rangeland forage production at specified spatial and temporal scales is necessary for grazing management and also for implementation of rehabilitation projects in rangelands. This study focused on the capability of a generalized regression neural network(GRNN) model combined with GIS techniques to explore the impact of climate change on rangeland forage production. Specifically, a dataset of 115 monitored records of forage production were collected from 16 rangeland sites during the period 1998–2007 in Isfahan Province, Central Iran. Neural network models were designed using the monitored forage production values and available environmental data(including climate and topography data), and the performance of each network model was assessed using the mean estimation error(MEE), model efficiency factor(MEF), and correlation coefficient(r). The best neural network model was then selected and further applied to predict the forage production of rangelands in the future(in 2030 and 2080) under A1 B climate change scenario using Hadley Centre coupled model. The present and future forage production maps were also produced. Rangeland forage production exhibited strong correlations with environmental factors, such as slope, elevation, aspect and annual temperature. The present forage production in the study area varied from 25.6 to 574.1 kg/hm^2. Under climate change scenario, the annual temperature was predicted to increase and the annual precipitation was predicted to decrease. The prediction maps of forage production in the future indicated that the area with low level of forage production(0–100 kg/hm^2) will increase while the areas with moderate, moderately high and high levels of forage production(≥100 kg/hm^2) will decrease both in 2030 and in 2080, which may be attributable to the increasing annual temperature and decreasing annual precipitation. It was predicted that forage production of rangelands will decrease in the next couple of decades, especially in the western and southern parts of Isfahan Province. These changes are more pronounced in elevations between 2200 and 2900 m. Therefore, rangeland managers have to cope with these changes by holistic management approaches through mitigation and human adaptations.
基金supported by National Natural Science Foundation of China (50575026, 50275013), National High-Tech. R&D Program for CIMS (2001AA412011).
文摘The definition of generalized product of fractal is first put forward for the research on the relations between original fractal and its product of fractal when the transformations of iteration function system (IFS) are incomplete. Then the representations of generalized product of IFS are discussed based on the theory of the product of fractal. Furthermore, the dimensional relations between the product of fractal and its semi-product are obtained. The dimensional relations of self-similar set are discussed. Finally, the examples for rendering fractal graphs are given. These results posses potentials in image compression and pattern recognition.
文摘Fermat’s last theorem, had the statement that there are no natural numbers A, B, and C such that A<sup>n</sup> + B<sup>n</sup> = C<sup>n</sup>, in which n is a natural number greater than 2. We have shown that any product of two odd numbers can generate Fermat or Pythagoras triple (A, B, C) following n = 2 and also it is applicable A<sup>2</sup> + B<sup>2</sup> + C<sup>2</sup> + D<sup>2</sup> + so on =A<sub>n</sub><sup>2 </sup>where all are natural numbers.
基金The National Natural Science Foundation of China( No. 10971188 )the Natural Science Foundation of Zhejiang Province(No.Y6110323)+2 种基金Jiangsu Planned Projects for Postdoctoral Research Funds(No. 0902081C)Zhejiang Provincial Education Department Project (No.Y200907995)Qiantang Talents Project of Science Technology Department of Zhejiang Province (No. 2011R10051)
文摘In order to study algebraic structures of parallelizable sphere s7, the notions of quasimodules and biquasimodnle algebras over Hopf quasigroups, which are not required to be associative, are introduced. The lack of associativity of quasimodules is compensated for by conditions involving the antipode. The twisted smash product for Hopf quasigroups is constructed using biquasimodule algebras, which is a generalization of the twisted smash for Hopf algebras. The twisted smash product and tensor coproduct is turned into a Hopf quasigroup if and only if the following conditions (h1→a) h2 = (h2→a) h1, (a←S(h1)) h2 = (a←S(h2)) h1, hold. The obtained results generalize and improve the corresponding results of the twisted smash product for Hopf algebras.
基金The National Natural Science Foundation of China(No.10871042)the Natural Science Foundation of Jiangsu Province(No.BK2009258)
文摘The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left weak H-module coalgebra.First,a weak generalized smash coproduct C×lH D over quantum groupoids is defined and the module and comodule structures on it are constructed.The weak generalized right smash coproduct C×rL D is similar.Then some isomorph-isms between them are obtained.Secondly,by introducing some concepts of a weak convolution invertible element,a weak co-inner coaction and a strongly relative co-inner coaction,a sufficient condition for C×rH D to be isomorphic to Cv D is obtained,where v∈WC(C,H)and the coaction of H on D is right strongly relative co-inner.Finally,the duality theorem for a generalized smash coproduct over quantum groupoids,(C×lH H)×lH H≌Cv(H×lH H),is obtained.
文摘Let k be a commutative ring, C a projective k-coalgebra. The smash productsof entwining structure (A, C)_ψ are discussed. When the map ψ is a bijective, and C is a finitelygenerated k-module, a version of the Ulbrich theorem for coalgebras C is given.
基金This work is supported by National Natural Science Foundation of Chinaby the excellent doctorate fund of Nanjing agricultural university
文摘This paper gives a sufficient and necessary condition for twisted products to be weak Hopf algebras, moreover, gives a description for smash products to be weak Hopf algebras. It respectively generalizes R.K.Molnar's major result and I.Boca's result.